Abstract-A method for construction of polar subcodes is presented, which aims on minimization of the number of lowweight codewords in the obtained codes, as well as on improved performance under list or sequential decoding. Simulation results are provided, which show that the obtained codes outperform LDPC and turbo codes.
A decoding algorithm for polar codes with binary 16 × 16 kernels with polarization rate 0.51828 and scaling exponents 3.346 and 3.450 is presented. The proposed approach exploits the relationship of the considered kernels and the Arikan matrix to significantly reduce the decoding complexity without any performance loss. Simulation results show that polar (sub)codes with 16 × 16 kernels can outperform polar codes with Arikan kernel, while having lower decoding complexity.
A decoding algorithm for polar (sub)codes with binary 2 t ×2 t polarization kernels is described. The proposed approach exploits the linear relationship of the considered kernels and the Arikan matrix. This relationship enables one to compute the kernel input symbol log-likelihood ratio (LLR) by computing path scores of several paths in Arikan successive cancellation (SC) decoding. Further complexity reduction is achieved by identification and reusing of common subexpressions arising in this computation. The proposed algorithm is applied to kernels of size 16 and 32 with improved polarization properties. It enables polar (sub)codes with the considered kernels to provide better performance and lower decoding complexity compared with polar (sub)codes with Arikan kernel.
A reduced complexity sequential decoding algorithm for polar subcodes is described. The proposed approach relies on a decomposition of the polar (sub)code into a number of outer codes, and on-demand construction of codewords of these codes in the descending order of their probability. The proposed algorithm can be also used for decoding of polar codes with CRC and short extended BCH codes. It has lower average decoding complexity compared to the existing decoding algorithms for the corresponding codes.where V is a (n − k) × n binary matrix, such that its rows end in distinct columns, and j i is the index of row with the last non-zero element in column i. Such symbols with non-trivial right hand side expressions are called dynamic frozen, and the corresponding codes are referred to as polar subcodes. Decoding of such codes can be implemented by a straightforward generalization of the successive cancellation algorithm and its derivatives.Properly constructed polar subcodes may have higher minimum distance than classical polar codes. This results in substantially better performance [3], [10] under the list SC algorithm and its derivatives. Polar codes with CRC [2] can be considered as a special case of polar subcodes.
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